Southeast Sustain, Paper Inc., produces two types of paper: paper for books and paper for magazines. Each ton of paper for books requires 2 tons of spruce and 3 tons of fir; each ton of paper for magazines requires 2 tons of spruce and 2 tons of fir. The company must supply at least 30,000 tons of paper for books and 10,000 tons of paper for magazines a year. The yearly availability of the materials is 278,000 tons of spruce and 426,000 tons of fir. The marketing department requires that the amount of paper manufactured for magazines be at least 1.5 times that is manufactured for books. The company's supply chain manager estimates the profit contribution as: $200 per ton for paper for books and $250 per ton for paper for magazines. Determine the amount of paper for books and the amount of paper for magazines to be produced in order to maximize the profit using linear programming technique. (IF YOU GET YOUR ANSWER IN FRACTION, PLEASE KEEP IT IN FRACTION)